Dual current controller of inverter interfaced renewable energy sources for accurate phase selection method and grid codes compliance

ABSTRACT

A method for correct operation of the current-angle-based phase-selection method (PSM) is based on a proper dual current controller (DCC) for inverter interfaced sources during unbalanced fault conditions. The fault type is determined in the inverter using voltage-angle-based PSM. Accordingly, fault-type zones&#39; bisectors of the current-angle-based are determined. Consequently, an initial negative-sequence current angle reference is determined to force the relative angle between the negative- and zero-sequence currents in the center of its correct fault-type zone. The initial positive-sequence current angle is determined according to reactive current requirements by grid codes. These initial angles are updated for accurate operation of the PSM and appropriate reactive current injection. Negative- and positive-sequence current references are determined in the stationary frame to comply with the reference angles and inverter&#39;s thermal limits. These references are regulated by a proportional-resonance controller.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention generally relates to inverter interfaced renewableenergy sources (IIRESs) and, more particularly, to an enhanced inverterinterfaced renewable energy sources controller to solve the problem indetecting faulted phase(s) for lines emanting from renewable energysources (RESs) and active distribution networks as well as provisioningthe grid with the possible reactive power requirements.

Background Description

IIRESs are pervading in both transmission and distribution networks dueto their benefits in terms of sustainability and being a clean source ofenergy. Thus, a large portion of fault currents measured by protectionrelays is supplied by IIRESs. However, the fault signatures for IIRESsdiffer from those of synchronous generators (SGs) as a SG is modeled bya voltage source behind a constant impedance, whereas an IIRES ismodeled as a controlled current source, which depends on the controllerobjectives and grid-codes requirements. These differences in faultcurrents signature lead to maloperation of the conventional protectionfunctions because they were designed based on the conventional SG model.Consequently, either the protection algorithms should be modified tocope with these exotic fault currents or the inverter should beaugmented with new objectives to generate fault currents capable ofoperating the traditional protection functions.

IIRES control is a crucial element for enabling renewable energy sources(RESs) to be integrated into the grid. Hence, several IIRES controllershave been proposed to enhance the grid during normal and faultconditions. IIRES control studies can be divided into low-level andhigh-level controls. Low-level control is responsible for synchronizingIIRES output current at different grid conditions and tracking thereference current with high dynamics, minimum overshoot, and minimumerror. In Yazdani and R. Iravani, Voltage-sourced converters in powersystems, Hoboken, N.J., USA, Wiley, 2010, a phase-locked loop (PLL) isdesigned based on a high order transfer function to guarantee highrobustness during unbalanced grid conditions. A PLL based on costfunction minimization for voltages in the stationary frame has beenproposed that reduces the calculation burden by eliminating therequirement for a rotating reference frame transformation. This methodhas been further enhanced by adding a filter to provide higher accuracyin contaminated grids. In another approach, second-order generalizedintegrator (SOGI) is used to extract the positive and negative-sequencecomponents under grid faults with high precision. Different currentcontrollers are analyzed in terms of computational burden, dynamicresponse, and harmonic compensation in yet another approach.

On the other hand, high-level control is responsible for determining theIIRES reference current which is classified according to the operationconditions into normal and fault conditions controllers. In normaloperation, the controller is mainly implemented to control thepositive-sequence current to extract the maximum power from RESs and tosupport the grid with ancillary services, such as reactive powersupport. In case of fault conditions, unbalanced voltages introduceseveral challenges to IIRES control. As a result, the IIRES controlleris enhanced by controlling the negative-sequence current, using dualcurrent controllers (DCCs), or controlling both the negative andzero-sequence current in transformerless IIRESs.

The DCCs aim to regulate both the positive and negative-sequence currentcomponents to enhance the operation of IIRESs by achieving specificobjectives. In general, the positive-sequence controller is designed toachieve the grid-codes requirements by injected reactive power accordingto the voltage dip percentage and to regulate the dc-link voltage to aconstant value. However, the former objective is mainly achieved byaugmenting the IIRES with a chopper circuit to dissipate the surplusinjected power from RESs which cannot be achieved by controlling theinverter currents only to avoid exceeding the thermal limits of theIIRES power-electronic components. On the other hand, thenegative-sequence-current controller is mainly implemented to achievespecific power quality objectives. For example, balancing the outputcurrents, eliminating active and reactive power oscillations, voltagesupport, and harmonic mitigations. One objective is injecting activepower to the grid at unity power factor and eliminating the active andreactive power oscillations without exceeding the IIRES maximum currentlimit. This is achieved by determining the maximum active power that canbe injected during fault to maintain the reference current lower thanthe maximum limit. In one approach, the sequence reference currents arecalculated to inject the desired active and reactive power into the gridwith minimum peak current, while in an alternative approach thereference current is calculated to control the reactive power andguarantee that phase voltages at the point of common coupling (PCC) arebetween their minimum and maximum limits.

Since IIRES output currents during fault conditions dramatically changeaccording to the controller objective, they can be modeled as a currentsource that differs from the conventional fault current signature ofSGs. Thus, the phase selection method (PSM) and other conventionalprotection functions are susceptible to failure for faults supplied fromIIRESs. The failure of PSM, which is used to determine the faultyphases, could affect the reliability of the electric power networks bydisconnecting healthy phases or affect the operation of other protectionfunctions, such as distance protection. Hence, researchers have proposedmodifications for the existing relays or changing the IIRES controllerobjective to enable robust operation for conventional PSM. E. Carrasco,M. Moreno, M. Martinez, and S. Vicente in “Improved faulted phaseselection algorithm for distance protection under high penetration ofrenewable energies,” Energies, vol. 13, no. 3, January 2020, utilize theconventional current-angle-based PSM, which is based on the relativeangles between the superimposed negative and zero-sequence currents(δ_(I) ⁰) and the negative and positive-sequence currents (δ_(I) ⁺),within a small time range. Thus, the current-angle-based PSM couldoperate in grids containing IIRESs. However, the proposed method failedto determine the faulted phase in part of the test cases and there is noguarantee that the IIRES controller will not affect the PSM during theproposed operation time. A. Hooshyar, E. F. El-Saadany, and M.Sanaye-Pasand in “Fault type classification in microgrids includingphotovoltaic DGs,” IEEE Trans. Smart Grid, vol. 7, no. 5, pp. 2218-2229,September 2016, propose determining the faulty phases based on thesuperimposed relative angles between the negative and zero-sequence andnegative and positive-sequence voltages which successfully determine thefaulted phases. However, this method requires changing the existencerelays making it an expensive solution. On the other hand, M. A. Azzouz,A. Hooshyar, and E. F. El-Saadany in “Resilience enhancement ofmicrogrids with inverter-interfaced DGs by enabling faulty phaseselection,” IEEE Trans. Smart Grid, 9(6): 6578-6589, November 2018,suggest controlling the negative-sequence current controller to mimicthe negative-sequence SG model which can be represented by a constantimpedance. M. A. Azzouz and A. Hooshyar, in“Dual current control ofinverter-interfaced renewable energy sources for precise phaseselection,” IEEE Trans. Smart Grid, 10(5):5092-5102, September 2019.propose controlling the negative-sequence current to operate either therelative angle between the negative and zero-sequence or the relativeangle between the negative and positive-sequence. In this method, theauthors determine the fault type by using voltage-angle-based PSM, thendetermine the proposed negative-sequence angle, which is used todetermine the negative-sequence current reference. It is worth notingthat both Azzouz et al. articles describe controlling the TIRES so thata portion of the conventional current-angle-based method could operatecorrectly but do not guarantee the robustness of the overall PSM indetermining the faulted phases.

Most researchers investigate solutions for the fault detectionmaloperation from the relay side by trying to find new algorithms tocope with these peculiar fault currents which require changing theexisting relays. However, these algorithms have not been validated todetermine the faulted phase(s) for different fault resistances and gridtopologies. On the other hand, recent researches propose to solve theproblem by controlling the inverter to have the same current signatureas synchronous generators (SGs). However, the proposed solutions onlyguarantee the operation for one method to determine the faulted phasebut do not guarantee that other existing relay algorithms will operatecorrectly with these proposed controllers. Thus, there is a vital needfor modifying IIRES's controller to guarantee the correct operation forthe PSM protection system.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to enhance inverterinterfaced renewable energy sources' (IIRESs') controller duringdifferent fault types, grid topologies, and fault resistances to solvethe traditional relays problem in detecting the faulted phase(s) forlines emanating from renewable energy sources (RESs) and activedistribution networks as well as provisioning the grid with the possiblereactive power requirements. The invention mimics the significant faultcurrent angles characteristics of the synchronous generator to operatethe traditional current-angle-based phase selection method (PSM) whileretaining the inverter's ability to control the reactive power injectedinto the grid within accepted boundaries. Thus, according to theinvention, both negative and positive-sequence-current angles arecontrolled to achieve a comprehensive solution for the problem.

The negative-sequence-current angle is determined based on the measuredzero-sequence-current angle and grid-codes (GCs) reactive powerrequirements in order to settle δ_(I) ⁰ in its correct zone fordetermining the fault phase(s) and update δ_(I) ⁺ to be as close aspossible from its correct zones with maintaining the positive-sequencecurrent to satisfy the reactive power requirements. This is achieved bydetermining the fault type at the IIRES side and calculating thezero-sequence-current angle, then determining the requirednegative-sequence-current angle to settle δ_(I) ⁰ in its proper zonecenter angle. Then, it is further updated according to the reactivepower requirements with a maximum shift (μ⁰) to correct δ_(I) ⁺operation without the failure of δ_(I) ⁰. On the other hand, thepositive-sequence-current angle will be modified by the minimum possibleangle to inject the most appropriate reactive power according to thegrid code requirements with the ability to settle δ_(I) ⁺ in its correctzone. In addition, the invention controls both the positive andnegative-sequence-current angles in the stationary frame (alpha-betaframe) instead of the synchronous frame (d-q frame), which reduces thenumber of the required controllers from four to two controllers andeliminates the requirement for determining the grid synchronous angle,which is difficult to be accurately detected in grids with largeharmonics contents. Thus, the results of the controller are moreaccurate. Besides, the reference current in the synchronous frame iscontrolled using a proportion resonance (PR) controller which possessesa better dynamic response than the PI controller in the stationaryframe. Thus, the controller could reach its desired reference anglesfaster which consequently decreases the relay delay time.

The invention provides a new perspective for controlling inverters,which is based on solving the problem of improper operation of the relayin detecting the faulted phase(s) with an endeavor to keep thesubstantial features of the inverter to enhance the voltage profileduring faults. Thus, the invention avoids changing the relay algorithmswhich requires replacing the existing relays in the grid because solvingthe problem from the relay side is considered an expensive solution.Besides, it will operate both δ_(I) ⁰ and δ_(I) ⁺ correctly comparedwith other proposed inverter controllers that either operate δ_(I) ⁰ orδ_(I) ⁺. Moreover, the inverter controller takes into account thereactive power requirements. Finally, the inveter controller determinesthe reference currents in the stationary frame in order to reduce thenumber of controllers and to increase the controller speed.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects and advantages will be betterunderstood from the following detailed description of a preferredembodiment of the invention with reference to the drawings, in which:

FIG. 1 is a block and circuit diagram of IIRES interfacing the gridthrough an LC filter;

FIG. 2 are diagrammatic illustrations of current-angle-based PSM zonesfor (a) δ_(I) ⁰ and (b) δ_(I) ⁺;

FIG. 3 is a block diagram of a double second-order generalizedintegrator structure;

FIG. 4 is a flow diagram illustrating the procedures to determine∠I_(o,ref) ⁻ and ∠I_(o,ref) ⁺ which is compatible with thecurrent-angle-based PSM;

FIG. 5 are block diagrams of (a) alpha frame PR controller and (b) betaframe PR controller;

FIG. 6 is a block and circuit diagram of a sample test system;

FIG. 7 are graphs of measured quantities at AG fault at run atR_(flt)=50Ω: (a) δ_(I) ⁺, (b) δ_(I) ⁰, and (c) I_(Q);

FIG. 8 are graphs of measured quantities at AG fault at run atR_(flt)=10Ω: (a) δ_(I) ⁺, (b) δ_(I) ⁰, and (c) I_(Q);

FIG. 9 are graphs of measured quantities at AG fault at run atR_(flt)=5Ω: (a) δ_(I) ⁺, (b) δ_(I) ⁰, and (c) I_(Q); and

FIG. 10 are graphs of measured quantities at AG fault at run atR_(flt)=1Ω: (a) δ_(I) ⁺, (b) δ_(I) ⁰, and (c) I_(Q).

DETAILED DESCRIPTION THE INVENTION

The objective of the invention is operating the current-angle-based PSMat the relay side by taking into account the GC requirements. Thecurrent-angle-based PSM operates according to the values of δ_(I) ⁰ andδ_(I) ⁺. The fault type is detected according to the zones where theangles are settled. Thus, the inverter should control the output currentto track an appropriate reference value of δ_(I) ⁰ (δ_(I,ref) ⁰) andreference value of δ_(I) ⁺(δ_(I,ref) ⁺) which can operate thecurrent-angle-based PSM with the ability to control reactive powerwithin valid boundaries.

The dynamic model for an TIRES interfaced to the grid through an LC lowpass filter as shown in FIG. 1 can be represented in the stationary (αβ)frame as

$\begin{matrix}{{V_{\alpha\beta} - V_{o\;{\alpha\beta}}} = {{L_{f}\frac{{dI}_{\alpha\beta}}{dt}} + {R_{f}I_{\alpha\beta}}}} & (1) \\{{I_{\alpha\beta} - I_{o\;{\alpha\beta}}} = {C_{f}\frac{{dV}_{o\;{\alpha\beta}}}{dt}}} & (2)\end{matrix}$where L_(f), R_(f) and C_(f) represent the inductor, resistance, andcapacitor of the LC low pass filter, respectively; V and I are the IIRESterminal voltage and output current, respectively; and V_(o) and I_(o)are the voltage and the current at the point of common coupling (PCC),respectively. To control the positive and negative-sequences separately,the stationary frame is separated into positive and negative-sequenceswhich are given by

$\begin{matrix}{F_{\alpha\beta} = {{F_{\alpha\beta}^{+} + F_{\alpha\beta}^{-}} = {{F_{m}^{+}\begin{bmatrix}{\sin\left( {{\omega\; t} + {\angle\; F^{+}}} \right)} \\{- {\cos\left( {{\omega\; t} + {\angle\; F^{+}}} \right)}}\end{bmatrix}} + {F_{m}^{-}\begin{bmatrix}{\sin\left( {{\omega\; t} + {\angle\; F^{-}}} \right)} \\{\cos\left( {{\omega\; t} + {\angle\; F^{-}}} \right)}\end{bmatrix}}}}} & (3)\end{matrix}$where F is an arbitrary phasor which can represent a voltage or currentquantity, F_(m) is the magnitude of the phasor, ∠F is the phase angle ofF, ω is the angular frequency, and the superscripts + and − representthe positive and negative-sequence components, respectively. Bysubstituting for the positive and negative-sequence quantities in (3)into (1) and (2), the IIRES model in the positive and negativestationary frame can be represented by

$\begin{matrix}\left\{ \begin{matrix}{{V_{\alpha}^{+} - V_{o\alpha}^{+}} = {{{- \omega}\; L_{f}I_{\beta}^{+}} + {R_{f}I_{\alpha}^{+}}}} \\{{V_{\beta}^{+} - V_{o\;\beta}^{+}} = {{\omega\; L_{f}I_{\alpha}^{+}} + {R_{f}I_{\beta}^{+}}}} \\{{I_{\alpha}^{+} - I_{o\;\alpha}^{+}} = {{- C_{f}}V_{o\;\beta}^{+}}} \\{{I_{\beta}^{+} - I_{o\;\beta}^{+}} = {\omega\; C_{f}V_{o\alpha}^{+}}}\end{matrix} \right. & (4) \\\left\{ \begin{matrix}{{V_{\alpha}^{-} - V_{o\alpha}^{-}} = {{{- \omega}\; L_{f}I_{\beta}^{-}} + {R_{f}I_{\alpha}^{-}}}} \\{{V_{\beta}^{-} - V_{o\;\beta}^{-}} = {{\omega\; L_{f}I_{\alpha}^{-}} + {R_{f}I_{\beta}^{-}}}} \\{{I_{\alpha}^{-} - I_{o\;\alpha}^{-}} = {{- C_{f}}V_{o\;\beta}^{-}}} \\{{I_{\beta}^{+} - I_{o\;\beta}^{-}} = {\omega\; C_{f}V_{o\alpha}^{-}}}\end{matrix} \right. & (5)\end{matrix}$

The positive and negative-sequence controller is designed in five stagesas follows:

Stage 1: Determining the Initial Values of δ_(I,ref) ⁰ and δ_(I,ref)⁺(δ_(I,Iref) ⁰ and δ_(I,Iref) ⁺, Respectively).

The first step is determining the fault type at the inverter side byusing the voltage-angle-based PSM. This method is based on the relativeangles between the sequence voltages. The loci of δ_(V) ⁰ (i.e.,relative angle between the negative and zero-sequence voltages) suggesttwo fault types, thus, by further using δ_(V) ⁺ (i.e., relative anglebetween the negative and positive-sequence voltages), the fault typewill be specified accurately. Then, δ_(I,Iref) ⁰ and δ_(I,Iref) ⁺ arechosen according to the fault type to be settled in the center of thecurrent-angle-based PSM correct zones as shown in FIG. 2. For example,for an AG fault, both δ_(I,Iref) ⁰ and δ_(I,Iref) ⁺ are designated to bezero. However, in an ABG fault, δ_(I,Iref) ⁰ and δ_(I,Iref) ⁺ arespecified as 120° and 60°, respectively.

Stage II: Calculating the Initial Negative-Sequence-Current AngleReference at the PCC (∠I_(o,ref) ⁻).

∠I_(o,Iref) ⁻ is specified to enforce δ_(I) ⁰ to be equal δ_(I,Iref) ⁰at the transformer grid side which can be achieved from∠I _(o,Iref) ⁻=δ_(I,Iref) ⁰ +∠I _(og) ⁰+θ_(tr) ⁰  (6)where ∠I_(og) ⁰ is the zero-sequence-current angle at the transformergrid-side and θ_(tr) ⁰ is the phase shift introduced by the transformerconnection. In the case of delta/star transformer, the negative-sequencecurrent in the star side lags the current in the delta side by 30°.Thus, in order to enforce δ_(I,Iref) ⁰ to be correctly achieved at thetransformer grid side, θ_(tr) ⁰ is selected to be 30°.

∠I_(og) ⁰ in (6) is calculated from the instantaneous value ofzero-sequence-current (I_(og) ⁰) which is determined from the measuredcurrent phasors as

$\begin{matrix}{I_{og}^{0} = {{\frac{1}{3}\left( {I_{og}^{a} + I_{og}^{b} + I_{og}^{c}} \right)} = {I_{ogm}^{0}{\sin\left( {{\omega\; t} + {\angle\; I_{og}^{0}}} \right)}}}} & (7)\end{matrix}$where I_(ogm) ⁰ represents the magnitude of the zero-sequence current atthe transformer grid-side. Then, the zero-sequence current is convertedinto two orthogonal components using the double second-order generalizedintegrator (SO-SOGI) as shown in FIG. 3, where K1 and K2 are the SO-SOGIgains, I′ is the filtered output current, and q represents a 90° phaseshift from the input signal. Finally, the zero-sequence current angle isdetermined by

$\begin{matrix}{{\angle\; I_{og}^{0}} = {{\tan^{- 1}\left( \frac{- I_{{og}\bot}^{0}}{I_{og}^{0}} \right)} - {\omega\; t}}} & (8)\end{matrix}$where I_(og⊥) ⁰ lags I_(og) ⁰ by 90° while cot is determined from adigital clock to the overall controlled system.

Stage III: Generating the Reference Negative andPositive-Sequence-Current Angles at the PCC (∠I_(o,ref) ⁻ and ∠I_(o,ref)⁺, Respectively).

The process for determining ∠I_(o,ref) ⁻ and ∠I_(o,ref) ⁺ is shown inFIG. 4. First, the expected δ_(I) ⁺ at the transformer grid-side(δ_(I,e) ⁺) is calculated from (9) which represents the value of δ_(I) ⁺if ∠I_(o,ref) ⁻ equals ∠I_(o,Iref) ⁻ and ∠I_(o,ref) ⁺ equals thepositive-sequence-current angle compatible with the grid-coderequirement (∠I_(GC) ⁺).δ_(I,e) ⁺ =∠I _(o,Iref) ⁻ −∠I _(GC) ⁺−θ_(tr) ⁺  (9)where θ_(tr) ⁺ represents the phase shift added between the negative andpositive-sequence currents due to the transformer connection. Thepositive-sequence current is shifted by 30°, while the negative-sequencecurrent is shifted by −30° when transferred from the delta to star side,i.e., ∠I_(o) ⁺−∠I_(og) ⁺=30° and ∠I_(o) ⁻−∠I_(og) ⁻=−30°. Thus, θ_(tr) ⁺is set 60° to determine δ_(I,e) ⁺ precisely at the grid-side.

Then, the difference between δ_(I,e) ⁺ and δ_(I,Iref) ⁺ is checked. Ifδ_(I,e) ⁺−δ_(I,Iref) ⁺ is between the reduced δ_(I) ⁺ zone limits (±μ⁺)which are chosen to be ±10° to leave 5° extra margin from the zoneboundaries as the actual limits of δ_(I) ⁺ zone is +15°. It is worthnoting that the δ⁺ zone limits could be extended to ±30 to enhance thePSM reliability. Accordingly, μ⁺ can be extended to 25 to increase thecontroller ability to cope with different GCs. ∠I_(o,Iref) ⁻ and ∠I_(GC)⁺ will be maintained to be the final negative and positive-sequencereference current angles (∠I_(o,ref) ⁻ and ∠I_(o,ref) ⁺), respectively.Otherwise, ∠I_(o,ref) ⁻ and ∠I_(o,ref) ⁺ will be modified as follows. Ifδ_(I,e) ⁺−δ_(I,Iref) ⁺ is greater than μ⁺ and the required shift for∠I_(o,Iref) ⁻, i.e., δ_(I,e) ⁺−δ_(I,Iref) ⁺−μ⁺, is less than the reducedδ_(I) ⁰ zone limits (μ⁰) which is selected to be 25° to have a 5° marginfrom δ_(I) ⁰ actual zone limits. It is worth noting that the δ⁰ zonelimits could reach ±60 to enhance the PSM reliability. Accordingly, μ⁰can be extended to 55 to increase the controller ability to cope withdifferent GCs. ∠I_(o,ref) ⁻ is formulated as∠I _(o,ref) ⁻ =∠I _(o,Iref) ⁻−(δ_(I,e) ⁺−δ_(I,Iref) ⁺−μ⁺)  (10)However, if the required shift for ∠I_(o,Iref) ⁻ is greater than μ⁰,then both ∠I_(o,ref) ⁻ and ∠I_(o,ref) ⁺ are altered as follows:

$\begin{matrix}\left\{ \begin{matrix}{\angle_{o,{ref}}^{-} = {{\angle I_{o,{Iref}}^{-}} - \mu^{0}}} \\{{\angle I_{o,{ref}}^{+}} = {{\angle I_{GC}^{+}} + \left( {\delta_{I,e}^{+} - \delta_{I,{Iref}}^{+} - \mu^{0}} \right)}}\end{matrix} \right. & (11)\end{matrix}$On the other hand, if δ_(I,e) ⁺−δ_(I,Iref) ⁺ is less than −μ⁺ and therequired shift for ∠I_(o,Iref) ⁻, i.e., |δ_(I,e) ⁺−δ_(I,Iref) ⁺+μ⁺|, isless than μ⁰, then ∠I_(o,Iref) ⁻ is determined from∠I _(o,ref) ⁻ =∠I _(o,ref) ⁻−(δ_(I,e) ⁺−δ_(I,Iref) ⁺+μ⁺).  (12)However, if the required shift for ∠I_(o,ref) ⁻ is greater than μ⁰, thenboth ∠I_(o,ref) ⁻ and ∠I_(o,ref) ⁺ are modified as follows:

$\begin{matrix}\left\{ \begin{matrix}{{\angle\; I_{o,{ref}}^{-}} = {{\angle I_{o,{Iref}}^{-}} + \mu^{0}}} \\{{\angle I_{o,{ref}}^{+}} = {{\angle I_{GC}^{+}} + \left( {\delta_{I,e}^{+} - \delta_{I,{Iref}}^{+} + \mu^{0}} \right)}}\end{matrix} \right. & (13)\end{matrix}$

∠I_(GC) ⁺ in (9) is calculated in the stationary frame from the positivesequence which is compatible with the GC requirements as

$\begin{matrix}{{\angle I_{GC}^{+}} = {{\tan^{- 1}\left( \frac{- I_{{o\;\beta},{GC}}}{I_{{o\;\alpha},{GC}}} \right)} - {\omega\; t}}} & (14)\end{matrix}$where I_(oα,GC) and I_(oβ,GC) are the expected positive-sequencecurrents that satisfy GC requirements in alpha and beta frame at thePCC, respectively. I_(oα,GC) and I_(oβ,GC) are further determined fromthe active- and reactive-power requirements as follows:

$\begin{matrix}{\begin{bmatrix}I_{{o\alpha},{GC}} \\I_{{o\;\beta},{GC}}\end{bmatrix} = {{\frac{2}{3}\begin{bmatrix}\frac{V_{o\alpha}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\beta}^{+} \right)^{2}}} & \frac{V_{o\beta}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\;\beta}^{+} \right)^{2}}} \\\frac{V_{o\beta}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\beta}^{+} \right)^{2}}} & \frac{- V_{o\alpha}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\beta}^{+} \right)^{2}}}\end{bmatrix}}\begin{bmatrix}I_{P,{Limit}}^{*} \\I_{Q}^{*}\end{bmatrix}}} & (15)\end{matrix}$where I_(P,limit)* is the limited active power reference and I_(Q)* isthe desired reactive current. I_(Q)* is determined from the GCrequirements, while I_(P)* is determined by using a PI controller tokeep the dc-link voltage at its reference value. During a fault, thepositive current injected by the inverter may exceed the inverterthermal limits. Thus, the current should be limited to the inverterpositive thermal limit (I_(limit)*) which is in the range between 1.2and 1.5 pu. It is worth noting that the reactive current is moresignificant during fault conditions so the active current is limited asI _(P,max) ⁺=√{square root over ((I _(limit) ⁺)²−(I _(Q))²)}  (16)where I_(P,max)* is maximum active current emanating from the inverter.Finally, V_(oα) ⁺ and V_(oβ) ⁺ is determined from the stationary framevoltages as

$\begin{matrix}{\begin{bmatrix}V_{o\;\alpha}^{+} \\V_{o\;\beta}^{+}\end{bmatrix} = {\begin{bmatrix}I & {- q} \\q & I\end{bmatrix}\begin{bmatrix}V_{o\alpha} \\V_{o\;\beta}\end{bmatrix}}} & (17)\end{matrix}$where q represents a 90° phase shift, which is determined by using theSO-SOGI as illustrated in FIG. 3.

Stage IV: Determining the Alpha-Beta Reference Currents at the InverterTerminal

The negative-sequence-current reference (I_(ref) ⁻) is designed tosatisfy the negative-sequence current angle (∠I_(o,ref) ⁻) generated instage III and the IIRES thermal limit requirement (I_(limit) ⁻) which isselected to be 0.3 pu. First, I_(o,ref) ⁻ is determined in thenegative-sequence stationary frame based on ∠I_(o,ref) ⁻ as follows:

$\begin{matrix}\left\{ \begin{matrix}{I_{{o\alpha},{ref}}^{-} = {I_{o,{limit}}^{-}{\sin\left( {{\omega\; t} + {\angle\; I_{o,{ref}}^{-}}} \right)}}} \\{I_{{o\;\beta},{ref}}^{-} = {I_{o,{limit}}^{-}{\cos\left( {{\omega\; t} + {\angle\; I_{o,{ref}}^{-}}} \right)}}}\end{matrix} \right. & (18)\end{matrix}$where I_(oα,ref) ⁻ and I_(oβ,ref) ⁻ represent the alpha and betanegative-sequence-current references at the PCC, respectively, andI_(Limit) ⁻ is the maximum negative-sequence current at the PCC which isdetermined by solving a second-order equation determined from (5) and(18) by(I _(o,limit) ⁻)² +I _(o,limit) ⁻(2ωC _(f) V _(o) ⁻sin(∠I _(o,ref) ⁻ −∠V_(o) ⁻))+((ωC _(f) V _(o) ⁻)²−(I _(limit) ⁻)²)=0  (19)To compensate for the capacitor effect, I_(ref) ⁻ is finally formulatedin the negative-sequence stationary frame as

$\begin{matrix}\left\{ \begin{matrix}{I_{\alpha,{ref}}^{-} = {I_{{o\;\alpha},{ref}}^{-} + {\omega\; C_{f}V_{o\;\beta}^{-}}}} \\{I_{\beta,{ref}}^{-} = {I_{{o\;\beta},{ref}}^{-} - {\omega\; C_{f}V_{o\;\alpha}^{-}}}}\end{matrix} \right. & (20)\end{matrix}$where I_(α,ref) ⁻ and I_(β,ref) ⁻ represent the alpha and betanegative-sequence-current reference at the inverter terminal,respectively.

On the other hand, the positive-sequence-current reference (I_(ref) ⁺)is formulated to ensure that its angle (∠I_(ref) ⁺) is enforced togenerate the correct ∠I_(o,ref) ⁺ determined from stage III. First, thenew reactive-current reference (I_(Q,new)*) is calculated from (21)based on I_(P,limit)* and the angle between I_(o,ref) ⁺ and I_(P)*,i.e., ∠I_(o,ref) ⁺−∠V_(o) ⁺.I _(Q,new) *=I _(P,limit)*tan(∠I _(o,ref) ⁺ −∠V _(o) ⁺)  (21)Then, both I_(Q,new)* and I_(P,limit)* pass by a current limiter toavoid exceeding the IIRES thermal limits without changing its phaseangle. If I_(o,ref) ⁺ exceeds its maximum positive-sequence currentlimit at the point of common coupling (I_(o,limit) ⁺), then I_(Q,new)*and I_(P,limit)*are updated as

$\begin{matrix}\left\{ \begin{matrix}{I_{Q,{new},{limit}}^{*} = {I_{Q,{new}}^{*} \times \frac{I_{o,{limit}}^{+}}{\sqrt{\left( I_{Q,{new}}^{*} \right)^{2} + \left( I_{P,{limit}}^{*} \right)^{2}}}}} \\{I_{P,{new},{limit}}^{*} = {I_{P,{Limit}}^{*} \times \frac{I_{o,{limit}}^{+}}{\sqrt{\left( I_{Q,{new}}^{*} \right)^{2} + \left( I_{P,{limit}}^{*} \right)^{2}}}}}\end{matrix} \right. & (22)\end{matrix}$Subsequently, the positive-sequence-current references in the stationaryframeat the PCC (I_(oα,ref) ⁺ and I_(oβ,ref) ⁺) are obtained by

$\begin{matrix}{\begin{bmatrix}I_{{o\;\alpha},{ref}}^{+} \\I_{{o\;\beta},{ref}}^{+}\end{bmatrix} = {{\frac{2}{3}\left\lbrack \begin{matrix}\frac{V_{o\alpha}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\;\beta}^{+} \right)^{2}}} & \frac{V_{o\beta}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\beta}^{+} \right)^{2}}} \\\frac{V_{o\beta}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\beta}^{+} \right)^{2}}} & \frac{V_{o\alpha}^{+}}{\sqrt{\left( V_{o\alpha}^{+} \right)^{2} + \left( V_{o\beta}^{+} \right)^{2}}}\end{matrix} \right\}}\begin{bmatrix}I_{P,{new},{limit}}^{*} \\I_{Q,{new},{limit}}^{*}\end{bmatrix}}} & (23)\end{matrix}$Thereafter, the IIRES terminal positive-sequence-current references(I_(α,ref) ⁺ and I_(β,ref) ⁺) are expressed as follows:

$\begin{matrix}\left\{ \begin{matrix}{I_{\alpha,{ref}}^{+} = {I_{{o\alpha},{ref}}^{+} - {\omega\; C_{f}V_{o\;\beta}^{+}}}} \\{I_{\beta,{ref}}^{+} = {I_{{o\;\beta},{ref}}^{+} + {\omega\; C_{f}V_{o\alpha}^{+}}}}\end{matrix} \right. & (24)\end{matrix}$Finally, the alpha and beta reference currents at the inverter terminals(I_(α,ref) and I_(β,ref)) are determined by

$\begin{matrix}\left\{ \begin{matrix}{I_{\alpha,{ref}} = {I_{a,{ref}}^{+} + I_{\alpha,{ref}}^{-}}} \\{I_{\beta,{ref}} = {I_{\beta,{ref}}^{+} - I_{\beta,{ref}}^{-}}}\end{matrix} \right. & (25)\end{matrix}$

Stage V: Tracking the Reference Current.

The reference currents in the alpha and beta frame are controlled usinga proportional resonance (PR) controller as shown in FIG. 5 where itsparameters are determined based on the procedures in Yazdani et al.(ibid) and D. N. Zmood and D. G. Holmes in “Stationary frame currentregulation of PWM inverters ith zero steady-state error”, in IEEETransactions on Power Electronics, vol. 18, no. 3, pp. 84-822, 2003.

The invention was tested in Matlab/Simulink environment to validate itsability in operating the current-angle-based PSM correctly andmaintaining the GC requirements within permissible limits. FIG. 6illustrates the test system which normally operates at 34.5 kV and 60Hz. It consists of a 9.2-MW IIRES connected to bus 3 through adelta-star-ground transformer with rated power 14-MW and x=0.1 pu. Therated voltages for the IIRES and gird side are 4.16 kV and 34.5 kV,respectively. The system reference reactive power is determined by theNorth American GC in which the reference reactive current injected tothe grid (I_(Q)*) is zero. The system is tested for an AG fault fordifferent fault resistances to demonstrate the effectiveness of theproposed method.

For a fault resistance (R_(flt)=50Ω), δ_(I) ⁺ settles in the AG faultcorrect zone at −7°, as shown in FIG. 7. Since δ_(I) ⁺ settles correctlyin the AG zone and it is lower than 10° (μ⁺), the negative-sequencecurrent is maintained to place δ_(I) ⁰ at the zone bisector which can beverified by FIG. 7. In addition, I_(Q) remains zero during the fault asexpected from the GC requirements because the controller succeeds toenforce both δ_(I) ⁰ and δ_(I) ⁺ in their correct zones without the needto change the positive-sequence current angle. FIG. 8 represents thecase when R_(flt)=10 Ω, δ_(I) ⁺ is settled in the AG zone at −μ⁺ andδ_(I) ⁰ is located correctly in the AG fault zone at 20° which is stilllower than μ⁰. This implies that ∠I_(o,Iref) ⁻ is unable to operate bothδ_(I) ⁺ and δ_(I) ⁰, and thus, it is corrected by adding 20° to∠I_(o,Iref) ⁻. It is worth noting that δ_(I) ⁰ settles at a value lowerthan μ⁰, so there is no necessity to change the positive-sequencecurrent reference. Thus, I_(Q) preserves its GC requirement and is keptat zero. FIGS. 9 and 10 represent a small fault resistance conditionwhen R_(flt)=5Ω and 1Ω, respectively. For both cases, δ_(I) ⁺ and δ_(I)⁰ settle at μ⁺ and μ⁰ which determine correctly an AG fault with 5°preserved margin. To avoid δ_(I) ⁺ and δ_(I) ⁰ to surpass its zonelimits, the positive-sequence angle is modified leading to variationfrom the reactive power GC requirements. It is worth noting that the SGcurrent during high resistive fault is mainly active. However, when thefault resistance decreases, the fault current of the SG becomes mainlyreactive. Thus, as the fault resistance decreases, the injected reactivepower should increase to comply with the conventional SG behavior. Thisis illustrated using the absolute magnitude of I_(G) which equals 0.12pu in FIG. 9 but in FIG. 10 it increases to reach 0.72 pu.

From the foregoing, it will be appreciated that the invention solves theproblem of improper operation of the traditional current-angle-basedphase selection methood (PSM) without replacing existing relays thusmaking for a less expensive solution. The invention maintains importantfeatures of the inverter controller by keeping the inverter's ability toinject power during faults, which enhances the voltage profile of thegrid during faults.

While the invention has been described in terms of a single preferredembodiment, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theappended claims.

Having thus described our invention, what we claim as new and desire tosecure by Letters Patent is as follows:
 1. A method for securing acorrect operation of a current-angle-based phase-selection method (PSM)when fault currents are supplied from inverter interfaced renewableenergy sources (IIRESs), comprising: determining a fault type by aninverter; selecting initial current angle references; determiningcurrent angle references; determining a reference current in astationary frame; and tracking the stationary frame reference currentwith a proportional-resonance (PR) controller.
 2. The method accordingto claim 1, wherein the current-angle-based PSM is based on relativeangles between negative- and zero-sequence currents and negative- andpositive-sequence currents.
 3. The method according to claim 1, whereinthe IIRES is connected to a grid through a low-pass filter and atransformer.
 4. The method according to claim 3, wherein the transformeris a delta/star-ground transformer.
 5. The method according to claim 1,wherein the fault type determination is performed by avoltage-angle-based PSM, which is based on relative angles betweennegative- and zero-sequence voltages and negative- and positive-sequencevoltages.
 6. The method according to claim 1, wherein the initialcurrent angle references are selected by determining initial positive-and negative-sequence currents angles independently.
 7. The methodaccording to claim 6, wherein the initial positive-sequence currentangle is based on reactive current requirements by grid codes and activecurrent regulating a direct current (DC) link voltage.
 8. The methodaccording to claim 7, wherein the active current is determined by aproportional-integral controller augmented with a feedforward controllerto regulate the DC link voltage.
 9. The method according to claim 6,wherein the initial negative-sequence current angle is selected based onthe fault type and zero-sequence current angle measured at a grid sideto force a relative angle between negative- and zero-sequence currentsto be in the center of current-angle-based PSM correct fault-type zone.10. The method according to claim 9, wherein the zero-sequence currentangle is determined by converting a measured zero-sequence current intotwo orthogonal components using a double second-order generalizedintegrator (SO-SOGI).
 11. The method according to claim 1, wherein thereferences for negative- and positive-sequence current angles aredetermined to secure correct operation for the current-angle-based PSM.12. The method according to claim 11, wherein the current anglereferences comprising a negative-sequence current angle reference thatis determined by updating an initial negative-sequence current anglereference to have a proper relative angle, according tocurrent-angle-based PSM, between the negative- and zero-sequencecurrents and negative- and positive-sequence current.
 13. The methodaccording to claim 12, further comprising updating the initialnegative-sequence current angle reference in a manner limited by maximumand minimum shift angles to prevent violating fault-type zonerequirements for the relative angle between the negative- andzero-sequence current angles.
 14. The method according to claim 13,wherein the maximum and minimum shift angles are 25° and −25°,respectively.
 15. The method according to claim 11, wherein thepositive-sequence current angle reference is determined by updating itsinitial angle to guarantee that a relative angle between the negative-and positive-sequence currents are in a reduced current-angle-based PSMfault-type zone.
 16. The method according to claim 15, wherein thereduced current-angle-based PSM fault-type zone is determined byreducing current-angle-based PSM fault-type zones by a margin set at 5°.17. The method according to claim 15, wherein the initialpositive-sequence current angle is updated only if a required shift forthe initial negative-sequence current angle reference overrides eitherits maximum or minimum shift angles.
 18. The method according to claim1, wherein the reference currents are determined based on the negative-and positive-sequence current angle references and maximum thermallimits.
 19. The method according to claim 18, wherein the negative- andpositive-sequence maximum limits are set at 0.3 and 1.2 per unit,respectively.